1. Field of the Invention
This invention pertains generally to target tracking of underwater objects and more particularly to the tracking of multiple targets using distributed acoustic linear sensor arrays utilizing spatial matched filtering techniques that can combine different image features from different image data in a coherent manner.
2. Description of the Related Art
The delay curve Hough transform (DCHT) was developed based on the paradigm of track-before-detect and applied to image data collected from a single sensor array for target tracking and track parameter estimations. Two different kinds of target tracking ambiguities are associated with a single sensor array using DCHT. See, Stevens et al., APPLICATION OF THE HOUGH TRANSFORM TO ACOUSTIC BROADBAND CORRELATIONS FOR PASSIVE DETECTION AND LOCATION; NRL Mem. Rpt. NRL/MR/5580-92-7182, January 1993. One of them is the mirror track ambiguity and the other is the delay curve parameter ambiguity. It is well known that multiple sensor systems are required to address these problems.
The DCHT is closely related to techniques of classical passive dual-channel localization. It uses a pattern recognition technique, the Hough transform, to operate on a set of continuous snapshots of cross-correlation, i.e., broadband correlation, between the two channels and perform target detection and target track parameter estimation. A broadband signal source with a constant speed, moving along a linear track, can generate a correlation trace in a broadband correlogram. This correlation trace can be described by an analytic equation, called the delay curve, determined by the track direction, the closest point of approach (CPA) time t0, and the ration between the closest point of approach horizontal distance D and speed v. Taking advantage of this delay curve, the DCHT hypothesizes a group of potential delay curves; accumulates evidence for each delay curve by summing (integrating) the pixel values along each hypothesized delay curve; stores accumulated pixel values in the parameter space (also known as the Hough Space); and thresholds the accumulated pixel values to detect the delay curves. Since the detection is done in the parameter space, the parameters of the image feature are determined by the location of the peak.
When using multiple sensor systems, multiple targets generate multiple traces on different recordings produced from different sensor systems. The difficulties encountered using multiple sensors are well-known issues of data association, such as measure-to-measure association—how the target traces are formed and how they relate to the target's movement—; measurement-to-track association—which trace should be followed when target traces cross each other—; and track-to-track association—which target traces in different recording are associated with the same target. Different tracks with the same CPA time t0, track direction θ, and v/D ratio but different speeds v and CPA horizontal distances D can generate the same delay curve, and hence, the DCHT cannot differentiate among such tracks. Also, given a linear sensor array, for any track, a mirror track exists that is the mirror reflection of the original track with respect to the linear sensor array. Due to the inherent geometric symmetry in a linear array, these two tracks produce the same delay curve in the broadband correlogram; hence, the DCHT cannot distinguish these two tracks.
The DCHT as a constant-speed signal source moves along a linear track in the neighborhood of a dual-sensor system, the time delay between the signal arriving at the two sensors follows an analytic equation called the delay curve. The two sensor system can consist of two omnidirectional hydrophones, two halves of a split array, or two individual arrays. Assuming a plane wavefront arrival at two sensors at the same depth, Sevens et al., supra, showed that the equation of the delay curve is given by:
                              τ          ⁡                      (            t            )                          =                              τ            max                    ⁢                                                                      (                                                            v                      D                                        ⁢                                          (                                              t                        -                                                  t                          0                                                                    )                                                        )                                ⁢                cos                ⁢                                                                  ⁢                θ                            -                              sin                ⁢                                                                  ⁢                θ                                                                    1                +                                  (                                                                                    v                        D                                            ⁢                                                                        (                                                      t                            -                                                          t                              0                                                                                )                                                2                                                              +                                                                  (                                                  h                          D                                                )                                            2                                                                                                                              (        1        )            where τ(t) is relative time delay between the two received signals at time t; τmax is the length of the baseline divided by the signal propagation speed; t0 is CPA time; D is horizontal distance at CPA from the signal source to the midpoint of the sensor pair; h is depth difference between the signal source and the sensors; v is the signal source speed; θ is the track direction defined by the right-turn rule convention; and t is observation time.
From the analytic equation for the delay curve, Eq. (1), the delay curve Hough transformation can be defined mathematically as
                              f          ⁡                      (                                          v                D                            ,              θ              ,                                                t                  0                                ⁢                                  h                  D                                                      )                          =                              1            N                    ⁢                      ∫                          ∫                                                F                  ⁡                                      (                                          x                      ,                      y                                        )                                                  ⁢                                  δ                  ⁡                                      (                                          τ                      ⁡                                              (                                                  x                          ,                          y                                                )                                                              )                                                  ⁢                                  ⅆ                  x                                ⁢                                  ⅆ                  y                                                                                        (        2        )            where f(v/D, θ, t0, h/D) is the output of the DCHT; F(x,y) is pixel value in the correlogram at location (x,y); δ( ) is Dirac-delta function restricting the integration to the delay curve; N is the total number of pixels in the integration; x is horizontal offset in correlogram, and y is vertical offset in correlogram.
The target track is a function of five track parameters: v, θ, h, D, and t0. The delay curve is a function of the four delay parameters: θ, t0, and the ratios v/D and h/D. The DCHT is defined over the set of delay curves parameters, and thus the parameter space of the DCHT has only four dimensions: θ, t0, v/D, and h/D. Each dimension is independently sampled over an appropriate range for the tracks of interest. For simplification, the depth factor, h/D, is assumed to be a constant.
As previously discussed, two target-tracking problems are associated with a single linear array. The first problem is the so-called delay curve parameter ambiguity different target tracks with different track parameters, v, D, θ, t0, but having the same delay curve parameters, v/D, θ, t0, will produce the same delay curve in the correlogram, hence are indistinguishable in the correlogram. The second problem is the mirror effect. For every individual target track there exists a mirror track; because of geometrical symmetry, the target track and its mirror track are indistinguishable in the correlogram since they always have the same time delay to the two sensors.
FIGS. 1a and 1b shows an example of the delay curve parameter ambiguity. FIG. 1a shows the target-sensor geometry, and FIG. 1b shows its corresponding delay curve. Even though the target track 11 is a straight line, the delay curve 13 in the correlogram veers sharply. Two parallel dashed lines 15 and 17 representing tow different target tracks are also shown in FIG. 1a; these dashed track lines 15 and 17 indicate different target tracks but with the same delay curve parameters; same direction, same CPA lines, the same v/D ratio. To have the same v/D ratio, a target track with a longer CPA distance must have a higher target speed and vice versa. Because their delay curve parameters are identical, these different tracks generate exactly the same delay curve in the correlogram. Without additional information, the DCHT cannot differentiate between these tracks.
FIG. 2 shows the mirror effect; two target tracks are shown. One is the reference track 19; the other one is the mirror reflection 21 of the reference track 19. Although the mirror track 21 is geometrically distinct from the reference track 19, the linear array cannot differentiate between the two because the correlation trace generated by the mirror track 21 is exactly the same as that generated by the reference track 19. It is useful to note that a track and its mirror track will have opposite signs (positive and negative) with respect to the right-turn rule for determining track direction, discussed above.
From the foregoing discussion, both the target track 11 and delay curve 13 are characterized by the track parameters v, D, θ, and t0. Using the DCHT, the delay curve 13 can be detected from the broadband correlogram, and the corresponding parameters can be extracted. The target track 11 an be reconstructed, but with some degree of ambiguity. The delay curve 13 equation, Eq. (1), can be viewed as a mapping between the target track 11 space and the delay curve 13 space. This mapping, however, is not a one-on-one mapping. Instead, because of the delay curve 13 parameter ambiguity and the mirror effect, it may be a many-to-one mapping. The key problem is how to resolve this many-to-one mapping to recover the actual target track from the correlation trace in the correlograms. The answer lies in using multiple arrays.